The present invention relates to an apparatus and method for optimizing a Boiler-Turbine-Generator plant.
In a factory using boiler-turbine-generator energy plant (hereinafter referred to as a BTG plant) it is desired to operate the plant at an optimum condition in which an operating cost is minimum.
FIG. 18 shows a conceptual diagram of the BTG plant and FIG. 19 shows a common composition of the BTG plant in the industry field.
As shown in FIG. 18, plural (Xm) steam turbines T (hereinafter referred to simply as the turbines) are driven by the steam generated by boilers B using fuel such as oil, gas, coal, recovered black liquor, etc. The turbines T respectively drive generators G to generate electric power. The generated power from the generators G is supplied to process load. The reduced-pressure steam through the turbines T is supplied to process load. If the power from the generators G is not sufficient to meet the power demand of the process load, commercial electric power is also supplied to the load.
The common BTG plant comprises, as shown in FIG. 19, boilers B01 to B04, turbines T01 to T04, and process loads (steam) H and L. The boilers B01 and B02 use the easy output-controllable fuel such as oil, gas, etc., whereas the boilers B03 and B04 use the commercial fuel such as coal, recovered black liquor, etc.
The high-pressure steam generated by the boilers B01 and B02 is supplied to the high-pressure steam header SL, and the high-pressure steam generated by the boilers B03 and B04 is supplied to the high-pressure steam header SH. Turbines T01 and T02 are driven by the high-pressure steam supplied from the steam header SH and drive the generators G01 and G02. The turbines T03 and T04 are driven by the high-pressure steam supplied from the steam header SL and drive the generators G03 and G04. The extracted steam from the turbines T01 and T02 is supplied to a low-pressure steam header DH and is further supplied to the process load H. The extracted steam from the turbines T03 and T04 is supplied to a low-pressure steam header DL and is further supplied to the process load L. Here, the pressure of the high-pressure steam header SH is higher than that of the high-pressure steam header SL, while the pressure of the high-pressure steam supply header DH is higher than that of the high-pressure steam supply header DL.
A pressure-reducing valve RPV1 is connected with the steam headers SH and SL. A pressure-reducing valve RPV2 is connected with the steam headers DH and DL.
In the BTG plant, the incoming fuel/steam output characteristic of the boiler B is near-proportional as shown in FIG. 20.
Meanwhile, the incoming steam/power output characteristic of the turbine T has a non-linear characteristic called a valve point characteristic having several dents, as shown in FIG. 21. The connected point between the dents is called as a valve point. While the turbine performance curve submitted by the turbine manufacturer is drawn as an envelope on peak points (valve points)--a broken line --, this envelope line has differences from the actual curve--a solid line--in FIG. 21.
Optimizing operation of the BTG plant means operating at the optimum operation condition in which a steam division from the boilers B to the turbines T and an electric power supplied from the commercial power source to the process load are varied so that a total cost including a fuel cost and a cost for buying the electric power is minimum. The effect of optimizing operation will be explained in FIGS. 22 and 23.
It is assumed that, in FIG. 22, two turbines of the same characteristic are driven by a given total amount of steam (100 T/H).
While the steam is equally divided to the two turbines, i.e., a 50 T/H each, the total power output becomes EQU 200.times.50+200.times.50=20,000 kW
as shown in FIG. 23.
While the steam is divided to the two turbines, one at 40 T/H and the other at 60 T/H, the total power output becomes EQU 210.times.40+218.times.60=21,480 kW
as shown in FIG. 23.
Thus, 1480 kW (7.4%) more power output can be generated by varying the division ratio of the steam to the turbines.
The optimizing system, utilizing a mathematical formula which models the BTG plant, finds a cost minimum steam and power division, which meets the process load demands.
FIG. 24 is a function block diagram showing a typical BTG plant optimizing system. The system comprises a plant model defining section 32 and a total energy cost minimizing calculating section 31.
In section 32, the characteristics and the operable limits of turbines, boilers, pressure-reducing valves, etc., are defined as the constituent elements of the BTG plant model, as well as mass balance formula of power or stream in each pressure (high-pressure and low-pressure), which are supplied to the total energy cost minimizing point calculating section 31 as a premise conditions.
And next, process demands are given to section 31. Then, the calculation section 31 finds an optimum power and steam division ratio of the boiler/turbines satisfying the power/steam demands by using a linear programming (LP) scheme or a non-linear programming (NLP) scheme.
The conventional schemes such as LP and NLP have following weak points.
LP can be applied only to a linear model. It is necessary, therefore, to approximate a non-linear actual plant model to a linear model. Consequently, the accuracy of a solution is lowered through such approximation, so that the cost saving effect is small.
NLP can solve the multi-dimensional problem and, therefore, handle the non-linear plant model. However, when the model is non-convex, only a local optimum solution can be obtained.
Since a valve point characteristic of the turbine is non-linear and has multi-peaks, the non-linear programming scheme merely finds a local optimum point in the vicinity of an initial value of calculation, but cannot find the true optimum point (global optimum point), as shown in FIG. 25.
In order to obtain the true optimum point by using the NLP, the initial value and search method have to be modified to well-fit to the model. However, the search logic becomes more complicated when aiming at an optimum solution, and lots of time and labor are taken in tuning calculation parameters.
In searching the true optimum point by NLP, it is necessary to properly determine the initial value and search area.
The initial value is one of calculating parameters which determines a starting point of calculation. The following method is often used to determine the initial point.
i) using the current operating point
ii) utilizing a solution obtained by the LP
In searching method, the Lagrange multiplication method-plus-conjugate gradient method often used as NLP algorithm, the search area has to be tuned so that only a single peak or dent is included in the area.
FIG. 26 shows a relation among the linear solution, non-linear solution and true optimum solution.
In FIG. 26, the solution obtained by LP is located at "D". The solution obtained by the linear approximating method is located at "D'", but the solution on the true model is located at "D".
When the initial value is "K" in NLP, a local minimal point "A" is obtained in the vicinity of the starting point "K". Being greater than a true minimum point "T", "A" is a local minimum point.
"B" is an intentionally moved point by "L2" from the local minimum point "A" to find a better solution. If point "B" is located in a lower position than point "A", the minimum point is shifted to the point "B". A local minimum point "T" is obtained in the vicinity of point "B".
However, a point "C" spaced apart by "L1" is located in a higher position than point "A", there is no shift of the optimum point.
A proper search method for one model is not always proper to other models. Therefore, NLP's solution does not guarantee to reach a true optimum point "T".
Since NLP is based on such assumption that the model has a convex characteristic, it cannot solve the optimizing problem unless it is known whether there is a peak/dent (single) and whether the position of the peak/dent is located.
NLP only can find the local optimum point for a multi-peak problem containing a plural peak/dent such as non-convex characteristics in the case of the turbine control valve.
In the conventional optimizing system, therefore, the operation is done at the local optimum point and there is room for efficiency improvement up to the true optimum point.
NLP method is difficult to tune its calculation parameters such as initial value, search area, for the user-operator with no special knowledge of optimization computation. Therefore, it is impossible for the user-operator to do the system modification of the plant model corresponding to the BTG plant change.
Mentioned above, conventional optimizing systems for BTG plant operation only obtains a linear solution with poor accuracy or a non-linear solution (local optimum solution). Furthermore, it is difficult to, in NLP, tune the calculation parameters such as the initial value and search area.